Loudspeakers: Effects of amplifiers and cables - Part 4

[Part 1 begins with an overview of amplifiers, and discusses basic requirements for current and voltage output, and transient response. Part 2 discusses nonlinear distortions in amplifiers, as well as amplifier classes and modes of operation, beginning with Class A and AB. Part 3 covers Class D and other amplifier classes, output transistor types (MOSFET or BJT), and choosing an amplifier.]

6.8 Loudspeaker cables and their effect on system performance
Few subjects in the world of audio systems excite so much controversy and heated debate as the subject of loudspeaker cables. A truly enormous amount of pseudo-science has been written about this subject, and, once again, so many cases have been reported which have tried to extrapolate from the specific to the general case, which is clearly nonsense.

In the world of high fidelity, there are many esoteric designs of amplifiers and loudspeakers which do not show the robustness of more typically professional equipment, and they tend to be used in domestic circumstances where electrical installations will not have been made with the type of attention to detail that would be found in a top professional recording studio. In some of these cases, a certain cable may clean up a sound, but the same cable in different circumstances, such as when used with professional equipment with clean electrical supplies, may not lead to any sonic improvement whatsoever.

Granted, an inadequate cable can certainly degrade a system, but there is no justification for using inadequate cables if serious listening is contemplated. So, perhaps we should look at what we mean by adequate.

6.8.1 The bare minimum
A loudspeaker cable, like an electrical power cable, needs to have a current carrying capacity such that it will not overheat, and a voltage insulation such that it will not arc, but the current carrying capacity of a loudspeaker cable cannot be calculated from the simple W = I2R formula that would apply to the wiring of an electric heater. What is more, loudspeaker cables may be carrying 11 octaves of frequency range and not just the single frequency of an electrical supply, so what happens over the whole range of operation is of interest, and all frequencies must be passed as uniformly as possible.

In the case of the vast majority of transistor amplifiers we are dealing with what amounts to a constant voltage source. This means that from the minimum rated load impedance up to infinity, the output voltage of the amplifier, for any given input voltage and at any frequency within its range, will be independent of the load to which it is connected. However, this is not the case with valve (tube) amplifiers, whose output loads must be critically matched to the output impedance of the valves, usually via a relatively complex output transformer, but for now we will restrict our discussion to the more typical transistor amplifiers.

In order to behave as a voltage source, and remain independent of load, the output impedance of the amplifier needs to be very low indeed - typically hundredths of an ohm. The ratio of the load impedance to the output impedance gives us the damping factor, which is an indication of the ability of the amplifier to suppress the natural resonances within a loudspeaker.

This electrical damping effect can be easily tested by lightly tapping the cone of a low frequency loudspeaker with the amplifier connected but turned off, then comparing the sound by tapping again with the amplifier switched on. A significantly deader sound should be heard in the latter case, when the near zero output impedance of the amplifier short circuits the voice coil. A similar effect can be demonstrated without an amplifier, simply by connecting a wire between the loudspeaker terminals, thus short-circuiting the coil.

When a loudspeaker diaphragm is struck, it behaves like a microphone. In fact, when a loudspeaker is connected to a microphone pre-amplifier input it makes quite a good microphone. The movement of the diaphragm in response to vibrations in the air moves the coil within the field of the magnet, which generates a voltage across the terminals. If the terminals are short-circuited, a current flows which tends to drive the voice coil in a direction which opposes the resonant movement of the diaphragm.

The shorted coil acts as a dynamic brake. The damping effect of an amplifier can greatly 'tighten up' the sound of the bass, because it allows the amplifier to better control the resonant movement of the low frequency drivers. In other words, the transient response is improved. The need for a very good short circuit is important, so if the resistance/impedance of a loudspeaker cable is not close to zero, the damping will not be as close to perfect as possible, and therefore the effect of the amplifier on the loudspeaker resonance will be reduced.

When dealing with such low impedances as are found in typical loudspeaker circuits, such as 4 ohms or less, we are dealing with impedances much lower than would normally be encountered in general electrical wiring. In order to achieve a moderately good damping factor of 40 on a 4 ohm load, the total of the series impedance exhibited by both the amplifier output impedance and the cable impedance could not exceed one tenth of an ohm.

The principal concern of an electrical engineer, when choosing a gauge of cable, is that it will pass the required current without either overheating and producing a fire risk, or causing a voltage drop due to its predominantly resistive impedance (at 50 or 60 Hz) which would reduce the effectiveness of the device to which it is connected. So, if the motor is running at its correct speed and the cable is stone cold, then that is more or less the end of the story from an electrician's point of view.

Conversely, far from dealing with a fixed voltage at a single frequency, a loudspeaker cable has an impedance which may be dominated by its resistance only at low frequencies. At high frequencies the inductance can be contributing more to the impedance than the resistance, and a loudspeaker working on the end of a 10 metre cable producing the same SPL as when connected to the output of the amplifier with 50 cm of cable is no indication that the cable is lossless.

If a cable has a resistance of 1 ohm and is connected to an 8 ohm loudspeaker, the voltage drop across the cable would be one part in 9 (i.e. across 1 ohm out of 9 ohms total). This represents about 11%, or about 1 dB, which would be barely audible.

For a voice announcement installation, such a cable may be entirely acceptable, but for a high quality music system it would impose a serious limit on the damping factor, and hence on the accuracy of the transient response at low frequencies. The subsequent resonance due to the loss of damping may even restore the 1 dB loss of perceived volume, but the nature of the sound would have changed.

From the point of view of the loudspeaker, the cable is a part of the output impedance of the amplifier, and the damping factor is defined by:

Z load
————
Z source

In other words, the load impedance divided by the output impedance. Therefore, if an 8 ohm load was connected directly to an amplifier having an output impedance (source impedance) of 0.1 ohm, the damping factor would be 8/0.1 or 80. If the two were now connected by a cable having a resistance of 1 ohm, the damping factor would be dependent on the combined resistance of the source and the cable: 1 + 0.1 ohms. The resulting damping factor would be:

8
— = 7.2
11

which in audio engineering terms is poor, and likely to lead to subjectively woolly bass.

At higher frequencies, the drive units which are used do not generally have the mass or compliance to freely resonate, and are additionally resistively damped by the air load. However, at these frequencies the cable inductance can behave like a frequency dependent resistor, and act as a filter. When used with loudspeakers which present variable impedance loads with relation to frequency, both the resistance and the reactive components of the impedance can act as potential dividers, giving rise to a frequency response that varies according to the relative values of cable impedance and loudspeaker input impedance. The loudspeaker response will then vary in different ways as cable length is varied.

Cables also have capacitance between the conductors, but this is not usually problematical because the capacitive reactance is so low compared to the impedances of loudspeaker circuits that its effect would not normally become apparent until hundreds of kilohertz. However, it has been known to affect some marginally stable amplifiers, although it could be said that these problems should be solved at source. Some cables are intentionally capacitive, up to 0.2 microfarads, to maintain the high frequency response at the loudspeaker terminals, but they may unpredictably alter the performance and stability of amplifiers.